Linear Instability Analysis on Compressible Navier-Stokes Equations with Strong Boundary Layer

A classical problem in fluid mechanics concerns the stability and instability of different hydrodynamic patterns in various physical settings, particularly in the high Reynolds number limit of laminar flows with boundary layers. Despite extensive studies when the fluid is governed by incompressible Navier-Stokes equations, there are very few mathematical results on the compressible fluid. This paper aims to introduce a new approach to studying the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime, where a subtle quasi-compressible and Stokes iteration is developed. As a byproduct, we show the spectral instability of subsonic boundary layers.